Lecture_7_Macroparasites2

Lecture_7_Macroparasites2 - 1/29/2009 Population biology of...

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1/29/2009 1 Population biology of macroparasites II: regulation, stability and causes of aggregation Basic Macroparasite Model Birth ( b- δ ) dH dt abH P =− − + ()( ) αδ dP dt WH P P H k k =− + + + βμ α () 2 1 dW P W WH = λ γ β b dH dP a la Dobson & Hudson Host Population (H) Adult Parasites (P) μ + d + d+ Parasite transmission ( H) death Free-living Larvae (W ) death death dt A note on notation You can not assume that the same Greek letter in a different paper means the same thing! (especially, but not only, if they were written by different authors they were written by different authors) Regulation and Stability Regulation: Birth rates decrease, or death rates increase, with increasing population size As population increases its growth is As population increases, its growth is limited Stability: Tendency to return to same equilibrium value when ‘perturbed’ away Population size returns to equilibrium and does not cycle Regulation of hosts by parasites? P H d b dt dH ) ( ) ( + = Host grows exponentially in absence of parasite (if b > d) dH/dt = 0 when (b-d) = P/H( α + δ ) If ( α , δ ) > 0, then parasites affect host abundance If P > 0, then parasites affect host abundance *) If α too high then no regulation If α too low then no regulation Regulation of host by macroparasite Depends on virulence ( α ) and degree of aggregation (k) Moderately virulent Host equilibrium (H* Virulence Random Aggregated k too low (extremely aggregated) no regulation
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1/29/2009 2 Effect of parasite aggregation Lets look at this again Regulation of hosts by macroparasites + + + = k k H P d P WH dt dP 1 ) ( 2 α μ β Lets look at this again: When aggregated e.g.
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Lecture_7_Macroparasites2 - 1/29/2009 Population biology of...

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